Problem: Simplify the following expression: $\sqrt{3} + \sqrt{12}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{3} + \sqrt{12}$ $= \sqrt{3} + \sqrt{4 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{3} + \sqrt{4} \cdot \sqrt{3}$ $= \sqrt{3} + 2\sqrt{3}$ Finally, simplify by combining the terms. $= ( 1 + 2 )\sqrt{3} = 3\sqrt{3}$